A die is thrown twice, what is the probability that atleast one of the two numbers is 6 ?

Options

A. `11/12`
B. `11/36`
C. `1/6`
D. `7/36`

Answer

To solve the problem of finding the probability that at least one of the two numbers rolled on a die is a 6, we can follow these steps:

### Step 1: Understand the Total Outcomes
When a die is thrown twice, the total number of outcomes can be calculated as:
- Each die has 6 faces.
- Therefore, when thrown twice, the total outcomes = 6 (for the first die) × 6 (for the second die) = 36.

**Hint:** Remember that the total outcomes for multiple events can be found by multiplying the number of outcomes for each event.

### Step 2: Calculate the Probability of the Complement Event
Instead of directly calculating the probability of getting at least one 6, we can calculate the probability of the complementary event (not getting a 6 in both throws) and then subtract it from 1.

- The probability of not getting a 6 on a single throw = 5/6 (since there are 5 other outcomes: 1, 2, 3, 4, 5).
- Therefore, the probability of not getting a 6 in both throws = (5/6) × (5/6) = 25/36.

**Hint:** The complement rule states that P(A) + P(not A) = 1, where A is the event of interest.

### Step 3: Calculate the Probability of Getting At Least One 6
Now, we can find the probability of getting at least one 6 by subtracting the probability of not getting a 6 from 1:
- P(at least one 6) = 1 - P(not getting a 6 in both throws)
- P(at least one 6) = 1 - (25/36) = 11/36.

**Hint:** Always check if you can simplify your calculations by using the complement of the event you're interested in.

### Final Answer
The probability that at least one of the two numbers rolled on a die is a 6 is **11/36**.

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